Cooling more does not increase the performance of a processor, but it does leave more headroom for overclocking. It doesn't increase the speed of the electrons, but it decreases the resistance and capacitance of the circuits, leading to faster gate switching (lower propagation delay). With faster switching gates, the clock period is reduced, which means the clock speed can be increased.
Better cooling also extends the life of a processor. It's analogous to an engine--the better you cool it, the less wear and tear there is on the internal components due to heat.
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